Posts Tagged ‘Conway’

Conway’s Game of Life

Tuesday 4 November 2008

Ever since the Sun xlock screensaver program at my university I have been fascinated by the visual display of Conway’s Game of Life. The screensaver shows a 2 dimensional grid of Sun logo’s where the pattern evolves in iterations according to a simple rules:

  1. Any live cell with fewer than two live neighbours dies, as if by loneliness.
  2. Any live cell with more than three live neighbours dies, as if by overcrowding.
  3. Any live cell with two or three live neighbours lives, unchanged, to the next generation.
  4. Any dead cell with exactly three live neighbours comes to life.

To get an idea how it works watch this short video:

The starting pattern determines how the cells evolve in each iteration. There are four possibile end states:

  1. a stable static end state
  2. a stable end state where the pattern comes back to the same state after a fixed number of iterations
  3. complete extinction, where no cells are populated
  4. an end state that is unlimited, meaning new cells are generated.
conway_glider1

Glider

Number 3 is the end state for most starting patterns. Very specific start sets are required to arrive at state 1 or 2. An ever growing end state is sort of a mathematical problem and Conway wrongfully assumed that no initial pattern could grow unlimited. Conway offered a $50 prize to the first person who could prove or disprove the conjecture before the end of 1970. Bill Gosper was the lucky guy to be the first to find one and both win the prize and to have the pattern named after him: the Gosper Gun. It is a pattern that after a few periods emits a so called glider (see image to the right).

There  are many free programs allowing you to inspect and play with Conway’s game of life. For example: